406310: GYM102354 A Square Root Partitioning

Consider the following expression: $$$$$$\sqrt{a_1} \pm \sqrt{a_2} \pm \dots \pm \sqrt{a_n} = 0\text{.}$$$$$$ Calculate the number of ways to replace each $$$\pm$$$ with $$$+$$$ or $$$-$$$ so that it holds true.

The first line of input contains a single integer $$$n$$$ ($$$2 \leq n \leq 36$$$).

Second line of input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 10^{10^5}$$$).

Output a single integer: the answer to the problem.

3
2 2 8

1

4
4 9 25 49

0